There is no reason for them to not give you a copy of the Summary Plan Description (SPD) upon request. It will at least give you some idea who distributions work although it might not address Alt Payee directly. You have a right to an SPD. So I would push for one.
I would ask them again to describe to you when they think you can start to be paid. Be aware if the stock isn't publicly traded on an exchange they might not know the current stock price until it is appraised. That can take months in the best of plans and until the summer for most. They should be able to give you a general idea. Something like "...we typically make the payments in the fall and it is our understanding you will get distribution forms then."
In the end, once you get the SPD if they really just refuse to work with you the SPD will describe who you send a formal written claim for benefits. Once you start the process they are obligated to tell you if you are due a benefit or not and why/why not. Send a written claim for benefits certified mail and compel them to at least reply to you.
Lastly, you can always file a complaint with the DOL. I never recommend going to them first. It is a pretty hostile move and people tend to lawyer up in response. Also, it is the government, so it doesn't move fast. There is also a good chance they are following the law and plan document just no communicating that fact well so you might not get the response you want.